Finite Group Databasebeta

← #14781681

Subgroups — #14781681

Order 2816.

1358 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623353C211yesmaximal, characteristic
2C2×#10622738C211yesmaximal, characteristic, complemented
3C2×#10622746C211yesmaximal, characteristic, complemented
4C2×#10622845C211yesmaximal, characteristic, complemented
5C2×#10622745C211yesmaximal, characteristic, complemented
6#13069914C214yesmaximal, complemented
7#13069907C214yesmaximal, complemented
8C2×#10622192C211yesmaximal, characteristic, complemented
9C11×#2879C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C2×#67004C2212yes—
15#10623353—24no—
16#10623353—24no—
17C2×#67003—22no—
18C2×#67002C2212yes—
19C2×#66995—21no—
20C2×#66985—21no—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C11×#408—22no—
25C11×#408C2214yes—
26C11×#407—22no—
27#10622845—22no—
28#10622845C2214yes—
29C2×#66899—21no—
30C2×#66896—21no—
31C2×#66888C2212yescomplemented
32#10622746—22no—
33#10622746—22no—
34#10622745—24no—
35C2×#66887C2212yescomplemented
36#10622738—24no—
37C2×#66885C2212yescomplemented
38C2×#66883C2214yescomplemented
39C2×#66880C2212yescomplemented
40#10622192C2214yescomplemented
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41D412yes—
48C2×C11×#41C2312yes—
49C22×Q8×C11D411yescharacteristic
50C22×D4×C11—21no—
51C22×D4×C11D411yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11—21no—
55C23×Dic11—21no—
56C2×#4339—22no—
57C2×#4339—21no—
58C2×#4339—21no—
59C2×#4339—21no—
60C2×#4339—21no—
61C2×#4339—22no—
62C2×#4339—22no—
63C2×#4339D414yes—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×Dic22C2311yescharacteristic
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C2×C11×M16—21no—
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C2×C11×M16D412yes—
73C2×C11×M16D412yes—
74C2×C11×M16C2312yes—
75C22×C8×C11—21no—
76C22×C8×C11C2312yes—
77#67004—24no—
78#67004—24no—
79#67003—216no—
80#67002—24no—
81#67002—24no—
82C2×#4326—22no—
83#66995—28no—
84C2×#4325—22no—
85C2×#4324—22no—
86#66985—28no—
87C2×#4323—22no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2312yes—
94C2×#4318—21no—
95C2×#4318—22no—
96C2×#4318—21no—
97C2×#4318—22no—
98C2×#4318—22no—
99C2×#4318D414yes—
100C2×#4318C2312yes—
101C2×#4318C2312yes—
102C22×C11⋊C8—21no—
103C22×C11⋊C8—21no—
104C11×C22⋊C8—28no—
105#66899—24no—
106#66896—24no—
107#66888—24no—
108#66887—24no—
109#66885—24no—
110#66883—28no—
111#66880—24no—
112#23533—111nomaximal, Sylow
113C24×C11—21no—
114C24×C11#4111yescharacteristic
115C23×D11—21no—
116C11×#41—24no—
117C11×#41—24no—
118C11×#41—22no—
119C11×#41—22no—
120C11×#41—22no—
121C11×#41—22no—
122C11×#41—42no—
123C11×#41—42no—
124C11×#41—42no—
125C11×#41—42no—
126C2×Q8×C11—21no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11C2×D412yes—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—21no—
134C2×D4×C11—22no—
135C2×D4×C11—42no—
136C2×D4×C11—42no—
137C2×D4×C11C2×D412yes—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11#4112yes—
150C22×C4×C11#4111yescharacteristic
151C22×C4×C11#4112yes—
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—24no—
154C2×C22⋊D11—41no—
155C2×C22⋊D11—41no—
156C2×C22⋊D11—42no—
157C22×Dic11—21no—
158C22×Dic11—22no—
159C22×Dic11—41no—
160C22×Dic11—41no—
161C22×Dic11—82no—
162#4339—24no—
163#4339—24no—
164#4339—24no—
165#4339—24no—
166#4339—42no—
167#4339—42no—
168#4339—42no—
169#4339—42no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44—21no—
175C2×D44C2×D412yes—
176C2×C4×D11—24no—
177C2×C4×D11—41no—
178C2×C4×D11—41no—
179C2×C4×D11—42no—
180C2×Dic22—21no—
181C2×Dic22—21no—
182C2×Dic22—21no—
183C2×Dic22—21no—
184C2×Dic22—21no—
185C2×Dic22C2×D412yes—
186C11×M16—24no—
187C11×M16—24no—
188C11×M16—22no—
189C11×M16—22no—
190C11×M16—42no—
191C2×C8×C11—22no—
192C2×C8×C11—22no—
193C2×C8×C11—22no—
194C2×C8×C11—42no—
195C2×C8×C11C2×D414yes—
196#4326—28no—
197#4325—28no—
198#4324—28no—
199#4323—28no—
200C4⋊Dic11—22no—
201C4⋊Dic11—22no—
202C4⋊Dic11—41no—
203C4⋊Dic11—41no—
204#4318—24no—
205#4318—22no—
206#4318—22no—
207#4318—22no—
208#4318—42no—
209#4318C2×D414yes—
210C2×C11⋊C8—24no—
211C2×C11⋊C8—22no—
212C2×C11⋊C8—22no—
213C2×C11⋊C8—42no—
214C2×#575—111no—
215C2×#430—111no—
216C2×#417—111no—
217C2×#417—111no—
218C2×#413—111no—
219#2879D1111yescharacteristic, complemented
220#2052—114no—
221#2051—114no—
222C2×#343—111no—
223C23×C11—22no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—42no—
227C23×C11—81no—
228C23×C11—81no—
229C23×C11#12111yescharacteristic
230C23×C11#12111yescharacteristic
231C23×C11#12312yes—
232C23×C11#12412yes—
233C23×C11C2×#4111yescharacteristic
234C22×D11—22no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—81no—
238C22×D11—81no—
239Q8×C11—22no—
240Q8×C11—22no—
241Q8×C11—42no—
242D4×C11—22no—
243D4×C11—22no—
244D4×C11—42no—
245D4×C11—42no—
246D4×C11—44no—
247D4×C11—42no—
248C2×C4×C11—22no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—44no—
253C2×C4×C11#12012yes—
254C2×C4×C11#12012yes—
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11#12112yes—
258C2×C4×C11#12112yes—
259C2×C4×C11#12112yes—
260C2×C4×C11#12112yes—
261C2×C4×C11#12312yes—
262C2×C4×C11#12312yes—
263C2×C4×C11#12312yes—
264C2×C4×C11#12412yes—
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C22⋊D11—44no—
272C22⋊D11—44no—
273C2×Dic11—22no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—42no—
277C2×Dic11—82no—
278C2×Dic11—82no—
279C2×Dic11—82no—
280D44—22no—
281D44—22no—
282D44—41no—
283D44—41no—
284C4×D11—44no—
285C4×D11—44no—
286Dic22—22no—
287Dic22—22no—
288Dic22—41no—
289Dic22—41no—
290C8×C11—24no—
291C8×C11—42no—
292C11⋊C8—24no—
293C11⋊C8—42no—
294C22×#41—111no—
295C22×#41C2×D1111yescharacteristic
296#575—224no—
297#575—224no—
298C2×#137—112no—
299C2×#137—221no—
300C2×AGL(1,ℤ/8)—112no—
301C2×AGL(1,ℤ/8)—221no—
302C2×#135—222no—
303C22×M16—111no—
304C22×M16—111no—
305C22×M16C2×D1111yescharacteristic
306C22×M16C2×D1111yescharacteristic
307C22×C4⋊C4—111no—
308#430—224no—
309C2×#108—114no—
310#417—114no—
311#417—222no—
312#417—222no—
313#417—222no—
314C2×#103—112no—
315C2×#103—221no—
316C2×#102—112no—
317C2×#102—221no—
318#413—224no—
319C2×#101—112no—
320C2×#100—112no—
321#408—22no—
322#408C2×D1114yes—
323#407—22no—
324#343—114no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—84no—
337C22×C11#39412yes—
338C22×C11#39412yes—
339C22×C11C2×#12111yescharacteristic
340C22×C11C2×#12311yescharacteristic
341C22×C11C2×#12411yescharacteristic
342C2×D11—42no—
343C2×D11—82no—
344C2×D11—81no—
345C2×D11—81no—
346C2×D11—82no—
347C4×C11—42no—
348C4×C11#39412yes—
349C4×C11#39412yes—
350C4×C11C2×#12011yescharacteristic
351C4×C11C2×#12111yescharacteristic
352C4×C11C2×#12111yescharacteristic
353C4×C11C2×#12311yescharacteristic
354Dic11—42no—
355Dic11—82no—
356C2×#41—21no—
357C2×#41—21no—
358C2×#41—22no—
359C2×#41—22no—
360C2×#41—22no—
361C2×#41—22no—
362C2×#41—114no—
363C2×#41—222no—
364C2×#41—221no—
365C2×#41—221no—
366C2×#41—222no—
367C2×#41—222no—
368C2×#41—221no—
369C2×#41—221no—
370C2×#41D4412yes—
371C2×#41C22×D1112yes—
372C22×Q8—111no—
373C22×Q8D4411yescharacteristic
374C22×D4—21no—
375C22×D4—111no—
376C22×D4—221no—
377C22×D4D4411yescharacteristic
378C23×C4—21no—
379C23×C4—221no—
380C23×C4—221no—
381C23×C4C22×D1111yescharacteristic
382#137—224no—
383#137—228no—
384#137—224no—
385AGL(1,ℤ/8)—224no—
386AGL(1,ℤ/8)—228no—
387AGL(1,ℤ/8)—224no—
388#135—2216no—
389C2×Q16—222no—
390C2×SD16—222no—
391C2×SD16—222no—
392C2×D8—222no—
393C2×M16—22no—
394C2×M16—22no—
395C2×M16—21no—
396C2×M16—22no—
397C2×M16—22no—
398C2×M16—114no—
399C2×M16—112no—
400C2×M16—112no—
401C2×M16—221no—
402C2×M16—222no—
403C2×M16—221no—
404C2×M16—222no—
405C2×M16—222no—
406C2×M16C22⋊D1112yes—
407C2×M16C22⋊D1112yes—
408C2×M16C22×D1112yes—
409C22×C8—21no—
410C22×C8—221no—
411C22×C8—221no—
412C22×C8C22×D1112yes—
413C2×C4⋊C4—112no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419#108—228no—
420#103—224no—
421#103—224no—
422#102—224no—
423#102—224no—
424#101—224no—
425#100—224no—
426C22⋊C8—28no—
427C2×C11—21no—
428C2×C11—21no—
429C2×C11—22no—
430C2×C11—22no—
431C2×C11—82no—
432C2×C11C2×#39411yescharacteristic
433C2×C11#306811yescharacteristic
434C2×C11#306911yescharacteristic
435D11—82no—
436C24—21no—
437C24—221no—
438C24#433911yescharacteristic
439#41—24no—
440#41—24no—
441#41—22no—
442#41—22no—
443#41—22no—
444#41—22no—
445#41—42no—
446#41—42no—
447#41—42no—
448#41—42no—
449#41—224no—
450#41—224no—
451#41—224no—
452#41—224no—
453#41—442no—
454#41—442no—
455#41—442no—
456#41—442no—
457C2×Q8—21no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—112no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8C2×D4412yes—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—112no—
475C2×D4—224no—
476C2×D4—221no—
477C2×D4—221no—
478C2×D4—221no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—442no—
482C2×D4—441no—
483C2×D4—441no—
484C2×D4C2×D4412yes—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—221no—
491C22×C4—224no—
492C22×C4—222no—
493C22×C4—442no—
494C22×C4—441no—
495C22×C4—441no—
496C22×C4—441no—
497C22×C4—441no—
498C22×C4—882no—
499C22×C4C2×D4411yescharacteristic
500C22×C4C2×D4411yescharacteristic
501C22×C4#433911yescharacteristic
502C22×C4D4×D1112yes—
503C22×C4D4×D1112yes—
504C22×C4#434112yes—
505C22×C4#434112yes—
506C22×C4C2×C22⋊D1111yescharacteristic
507C22×C4C2×C22⋊D1111yescharacteristic
508C22×C4C23×D1111yescharacteristic
509Q16—228no—
510SD16—228no—
511SD16—228no—
512D8—228no—
513M16—24no—
514M16—24no—
515M16—22no—
516M16—22no—
517M16—42no—
518M16—114no—
519M16—224no—
520M16—222no—
521M16—222no—
522M16—222no—
523M16—442no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—42no—
528C2×C8—224no—
529C2×C8—222no—
530C2×C8—222no—
531C2×C8—442no—
532C2×C8C2×C22⋊D1114yes—
533C4⋊C4—222no—
534C4⋊C4—222no—
535C4⋊C4—441no—
536C4⋊C4—441no—
537C11#2353311yescharacteristic, complemented, Sylow
538C23—22no—
539C23—41no—
540C23—41no—
541C23—42no—
542C23—81no—
543C23—81no—
544C23—222no—
545C23—441no—
546C23—441no—
547C23—881no—
548C23—881no—
549C23#6693612yes—
550C23#6693812yes—
551C23#6698311yescharacteristic
552C23#6698311yescharacteristic
553C23C2×#433911yescharacteristic
554Q8—22no—
555Q8—22no—
556Q8—42no—
557Q8—222no—
558Q8—222no—
559Q8—441no—
560Q8—441no—
561D4—22no—
562D4—22no—
563D4—42no—
564D4—42no—
565D4—44no—
566D4—42no—
567D4—222no—
568D4—222no—
569D4—444no—
570D4—444no—
571D4—441no—
572D4—441no—
573C2×C4—22no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—44no—
578C2×C4—222no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—444no—
582C2×C4—444no—
583C2×C4—442no—
584C2×C4—882no—
585C2×C4—882no—
586C2×C4—882no—
587C2×C4#6693512yes—
588C2×C4#6693512yes—
589C2×C4#6693612yes—
590C2×C4#6693812yes—
591C2×C4#6693912yes—
592C2×C4#6693912yes—
593C2×C4#6698311yescharacteristic
594C2×C4#6698311yescharacteristic
595C2×C4#6699112yes—
596C2×C4#6699112yes—
597C2×C4#6699212yes—
598C2×C4#6699212yes—
599C2×C4C22×D4411yescharacteristic
600C2×C4C2×D4×D1111yescharacteristic
601C2×C4C2×D4×D1111yescharacteristic
602C2×C4C2×#434111yescharacteristic
603C2×C4C2×#434111yescharacteristic
604C2×C4C22×C22⋊D1111yescharacteristic
605C8—24no—
606C8—42no—
607C8—224no—
608C8—442no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—84no—
621C22—442no—
622C22—882no—
623C22—882no—
624C22—881no—
625C22—881no—
626C22#1062257412yes—
627C22#1062257412yes—
628C22C2×#6693611yescharacteristic
629C22C2×#6693811yescharacteristic
630C22C2×#6698311yescharacteristic
631C4—42no—
632C4—442no—
633C4—882no—
634C4#1062257412yes—
635C4#1062257412yes—
636C4C2×#6693511yescharacteristic
637C4C2×#6693911yescharacteristic
638C4C2×#6699111yescharacteristic
639C4C2×#6699211yescharacteristic
640C2—22no—
641C2—21no—
642C2—21no—
643C2—22no—
644C2—82no—
645C2—882no—
646C2C2×#1062257411yescharacteristic
647C2#1307834411yescharacteristic
648C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2879C2
socleC22×C11C2×#121
prime radicalC2×#10623353C2
hypercenter#2879D11
hypocenterC11#23533
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2879

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#10622738C2semidirect
3. C2×#10622746C2semidirect
4. C2×#10622845C2semidirect
5. C2×#10622745C2semidirect
6. #13069914C2semidirect
7. #13069907C2semidirect
8. C2×#10622192C2semidirect
9. C11×#2879C2semidirect
31. C2×#66888C22semidirect
35. C2×#66887C22semidirect
37. C2×#66885C22semidirect
38. C2×#66883C22semidirect
39. C2×#66880C22semidirect
40. #10622192C22semidirect
219. #2879D11semidirect
537. C11#23533semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106233532
C2×#106227382
C2×#106227462
C2×#106228452
C2×#106227452
#130699142
#130699072
C2×#106221922
C11×#28792
#2353311